# User Contributed Dictionary

- past of triangulate

### Anagrams

# Extensive Definition

In trigonometry and geometry, triangulation is the
process of finding coordinates and distance to a
point by calculating the length of one side of a triangle, given measurements of
angles and sides of the triangle formed by that point and two other
known reference points, using the law of
sines.

In the figure at right, the third angle of the
triangle (call it θ) is known to be
180 − α − β,
since the sum of the three angles in any triangle is known to be
180 degrees. The opposite-side for this (the third) angle is l,
which is a known distance. Since, by the law of sines, the ratio
sin(θ)/l is equal to that same ratio for the other two angles α and
β, the lengths of any of the remaining two sides can be computed by
algebra. Given either of these lengths, sine and cosine can be used to calculate
the offsets in both the north/south and east/west axes from the
corresponding observation point to the unknown point, thereby
giving its final coordinates.

Some identities often used (valid only in flat or
euclidean
geometry):

- The sum of the angles of a triangle is π radians or 180 degrees.
- The law of sines
- The law of cosines
- The Pythagorean theorem

## Calculation

- α, β and distance AB are already known
- C can be calculated by using the distance RC or MC:

- RC: Position of C can be calculated using the Law of Sines

- \gamma=180^\circ-\alpha-\beta
- \frac=\frac=\frac

Now we can calculate AC and BC

- AC=\frac
- BC=\frac

Last step is to calculate RC via

- RC=AC \cdot \sin\alpha
- or
- RC=BC \cdot \sin\beta

- MC can be calculated using the Law of Cosines and the Pythagorean theorem

- MR=AM-RB=\left(\frac\right)-\left(BC \cdot \cos\beta\right)
- MC=\sqrt

Triangulation is used for many purposes,
including surveying,
navigation, metrology, astrometry, binocular
vision, model
rocketry and gun direction of weapons.

Many of these surveying problems involve the
solution of large meshes of triangles, with hundreds or even
thousands of observations. Complex triangulation problems involving
real-world observations with errors require the solution of large
systems of simultaneous
equations to generate solutions.

Famous uses of triangulation have included the
retriangulation of Great Britain.

## See also

- GSM localization
- Multilateration, where a point is calculated using the time-difference-of-arrival between other known points
- Parallax
- Real-time locating
- Resection
- SOCET SET
- Stereopsis
- Trig point
- Trilateration, where a point is calculated given its distances from other known points

triangulated in Bulgarian: Триангулация

triangulated in Czech: Triangulace

triangulated in German: Triangulation
(Geodäsie)

triangulated in Spanish: Triangulación

triangulated in French: Triangulation

triangulated in Croatian: Triangulacija

triangulated in Indonesian: Triangulasi

triangulated in Italian: Triangolazione

triangulated in Hebrew: טריאנגולציה

triangulated in Hungarian: Háromszögelés

triangulated in Dutch: Driehoeksmeting

triangulated in Norwegian: Triangulering

triangulated in Polish: Triangulacja
(geodezja)

triangulated in Russian: Триангуляция

triangulated in Slovenian: Triangulacija

triangulated in Swedish:
Triangulering